Abstract
We consider onset of transport (de-pinning) in one-dimensional bosonic chains with a repulsive boson–boson interaction that decays exponentially on large length-scales. Our study is relevant for (i) de-pinning of Cooper-pairs in Josephson junction arrays; (ii) de-pinning of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunneling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped onto an effective model of a one-dimensional elastic field in a disordered potential. The standard de-pinning theories address infinitely long systems in two limiting cases: (a) of uncorrelated disorder (zero correlation length); (b) of long range power-law correlated disorder (infinite correlation length). In this paper we study numerically chains of finite length in the intermediate case of long but finite disorder correlation length. This regime is of relevance for, e.g., the experimental systems mentioned above. We study the interplay of three length scales: the system length, the interaction range, the correlation length of disorder. In particular, we observe the crossover between the solitonic onset of transport in arrays shorter than the disorder correlation length to onset of transport by de-pinning for longer arrays.
Highlights
Depinning theory describes the onset of propagation in many different physical systems
It was recently shown that the onset of electrical transport in one-dimensional arrays of Josephson junctions is determined by the de-pinning of the charge-configuration along the array [7]
In the case that disorder is present in the system, de-pinning theory can be applied to find the critical driving force that leads to a steady boson transport through the system
Summary
Depinning theory describes the onset of propagation in many different physical systems. In this paper we consider a more general model, a discrete chain macroscopically occupied by bosons with a repulsive interaction that decays exponentially on long length-scales. In such a model the interaction between neighboring islands can be expressed by introducing a continuous variable, quasi-charge/flux, whose value is determined by the distribution of bosons along the chain. Our results describe the dual system of quantum phase slip (QPS) ladders In the latter case (QPS ladders) the bosons are magnetic flux quanta that tunnel through QPS elements [9,10,11] that separate the loops in a ladder
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